WASHINGTON -- Microsoft's fate in its epic antitrust battle may now depend on the very machine that the company helped make ubiquitous: a computer.

Wednesday, lawyers for Microsoft Corp. and the government file back into the courtroom of District Court Judge Thomas Penfield Jackson to begin the final stage of their landmark trial, which will determine the remedies Microsoft must face for violating antitrust laws. But lawyers on both sides already are looking beyond Judge Jackson's courtroom to the inevitable appeal, which will likely be heard by a three-judge panel of the D.C. Circuit Court of Appeals.

Under a standard procedure rarely breached in that appeals court, a computer will randomly assign the three-judge panel to the case from the court's six Republican and four Democratic appointees. That decision could prove crucial.

To date, the appeals judges have been a blessing for the software giant. In 1998, Judge Stephen Williams of the appeals court rejected a separate ruling against Microsoft by Judge Jackson, with a surprisingly harsh lecture about not second-guessing the software maker. Judge Jackson fired back last month, warning that such a view might put Microsoft beyond the reach of antitrust law.

And in 1995, an appeals court panel reinstated an earlier antitrust settlement with Microsoft that had been rejected by then-District Court Judge Stanley Sporkin for being too soft on the company. D.C. Circuit Court Judge Laurence Silberman, appointed in 1985 by President Reagan, wrote that Judge Sporkin had "overstepped his bounds" by rejecting the proposed settlement -- and ordered that the case be reassigned to another judge. Microsoft's lawyers can only hope Judge Williams or Judge Silberman will be among the chosen three.

But until the computer makes its choice, it will be way too early to celebrate in Redmond, Wash., Microsoft's hometown. For the nine justices on the D.C. court are a diverse bunch. Some are liberal, some conservative, some antitrust hawks, some free-market true believers. And court watchers predict the full Court of Appeals may never hear the case, instead choosing to speed the three-judge panel's decision directly to the Supreme Court.

Adding to those uncertainties is that the ultimate arbiter -- the Supreme Court -- hasn't laid down clear markers on some of the key issues in the case. The core of the government's case, for instance, is that Microsoft illegally tied Explorer, its Internet browser, to its software system to crush a competitor.

"There are statements that the Supreme Court has made that are consistent with Judge Jackson's approach and some that are consistent with Judge Williams's approach," observes Richard Pierce, a law professor at George Washington University School of Law. "That creates the classic opportunity for judges to hold widely disparate views on what the law is."

The D.C. circuit court judges, who are widely regarded as some of the nation's smartest, don't handle many big antitrust cases; those more commonly are brought under private lawsuits in other venues. Rather, the court's specialty is reviewing mind-numbing, complex administrative-law cases involving thousands of pages of regulatory actions from such government behemoths as the Federal Communications Commission and Environmental Protection Agency. So they won't be daunted by the breadth of the Microsoft case.

"In terms of its intellectual horsepower, it is as talented a court as exists in the country," says David Vladeck, the director of Public Citizen Litigation Group and currently a visiting professor at Georgetown Law School.

The intellectual horses also have warmer relations than they used to; a factor that could affect the outcome of the Microsoft case. For decades, the D.C. circuit was a battleground for bitter ideological warfare and personal acrimony. In the 1970s, some judges stopped speaking to each other after fights over whether the court's liberals were too soft on crime.

Chief Judge Harry Edwards, appointed in 1980 by President Carter, is widely credited with changing that. Every two months or so, for example, Chief Judge Edwards arranges social lunches with interesting guests, including retired Gen. Colin Powell. Recently, the judges chatted over chicken caesar salad with Daniel Snyder, the brash, multimillionaire owner of the Washington Redskins football team, about how much fun it is to own a sports team.

The socializing has a serious point. More cooperation among the judges is expected to help speed the Microsoft case to resolution. And less rancor means judges don't carry old professional disagreements into new cases, as their predecessors often did, people familiar with the court say.

Of course, geniality doesn't mean that ideology doesn't spill over into decision-making. Judges Douglas Ginsburg and Stephen Williams, both appointed by President Reagan in 1986, philosophically oppose what they view as government intervention in the marketplace. That includes some antitrust actions. Both men belong to a conservative school of thought known as "law and economy," which evaluates law from an economic standpoint to determine how a particular statute promotes the goals of maximizing wealth and increasing efficiency.

They would appear to be two votes for Microsoft -- if they are picked for the panel. But Judge Ginsburg, a former Justice Department Assistant Attorney General for antitrust, doesn't automatically take a pro-business stance. In the mid-1980s, when the Detroit News and Detroit Free Press, then in bitter competition, sought government relief through a special joint operating agreement, he objected strenuously.

"When a newspaper owner consciously and deliberately decides to sacrifice short-term profits in a quest for greater long-term profits, indeed potentially monopoly profits" why should the government help them out? he wrote.

Judge Williams, in his 1998 opinion, rejected Judge Jackson's preliminary injunction on Microsoft's Windows 98 software. Judge Williams also cautioned Judge Jackson against second-guessing decisions on product design by high-technology companies such as Microsoft, when they integrate new features into a product.

Judge Jackson, also a Reagan appointee, responded: "Read literally, the D.C. Circuit's opinion appears to immunize any product design ... from antitrust scrutiny, irrespective of its effects upon competition" as long as a company claims that the integration of new features is meant to enhance the product.

Countering the conservatives, President Clinton's three appointments to the circuit court generally tend to side with the government in such cases. A key member of that group is Judge David Tatel, who came to the court with a reputation as a liberal but -- his supporters insist -- now sometimes takes a more moderate stance. Last year, for instance, Judge Tatel sided with Judge Williams in reversing a ruling that prisoners had a constitutional right to have access to Playboy magazine.

Still, uncertainties remain. The Microsoft case could go directly from the U.S. district court to the Supreme Court, under a procedure that is rarely used, although that isn't considered likely.

And, warns, former D.C. Circuit Judge Abner Mikva, "One reason why judge-watching is a dangerous sport, is that the minute you think you've pegged them, they do the opposite thing."